Dynamics of interacting fermions in one dimension

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Abstract
The dynamics of a one-dimensional many-particle Fermi system containing one particle spin down (the d particle) in a sea of spin-up particles (u particles) is discussed in the context of an exactly solvable model problem. It is assumed that random variables associated with the d particle are relevant, and the marginal distributions of these random variables are calculated. The marginal distribution of the u-d relative coordinate is found to be constant in time and therefore to provide a connection of dynamics to equilibrium. This constant probability distribution affects the temperature-volume dependence of the partition function and, in the case of an attractive interaction, leads to a phase transition from an unpaired to a paired state at a well-defined critical temperature.

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